Wireless deep-subwavelength metamaterial enabling sub-mm resolution magnetic resonance imaging

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ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

jo u r n al hom e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

Wireless

deep-subwavelength

metamaterial

enabling

sub-mm

resolution

magnetic

resonance

imaging

Sayim

Gokyar

a,b,∗

_,

_Akbar

_Alipour

a,b

_,

_Emre

_Unal

a,b

_,

_Ergin

_Atalar

a

_,

_Hilmi

_Volkan

_Demir

a,b,c

a_Department_of_Electrical_and_Electronics_Engineering,_Department_of_Physics,_National_Magnetic_Resonance_Research_Center_(UMRAM),_Bilkent_University, Ankara,TR-06800,Turkey

b_{UNAM-National}_{Nanotechnology}_Research_Center_and_Institute_of_Materials_Science_and_{Nanotechnology,}_Bilkent_University,_Ankara,_TR-06800,_Turkey c_Luminous!_Center_of_Excellence_for_{Semiconductor}_Lighting_and_Displays,_School_of_Electrical_and_Electronic_Engineering,_School_of_Physical_and MathematicalSciences,PhysicsandAppliedPhysicsDivision,NanyangTechnologicalUniversity,Singapore

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received9May2017

Receivedinrevisedform4March2018 Accepted19March2018

Availableonline20March2018 Keywords:

Magneticresonanceimaging Metamaterials

Deep-subwavelengthresonators

a

b

s

t

r

a

c

t

Awirelessdeep-subwavelengthmetamaterialarchitectureisproposed,modeledanddemonstratedfora high-resolutionmagneticresonanceimaging(HR-MRI)applicationthatisminiaturizedtoberesonantat approximately␭0/1500dimensions.Theproposedstructurehastheadjustableresonancefrequencyfrom

65MHzto5.5GHzforthesub-cmfootprintarea(8mm×8mmforthisstudy)andprovidesaqualityfactor (Q-factor)ofapproximately80infreespacefor123MHzofoperation.Thisstructureconsistsofacross-via metallizedpartial-double-layermetamaterial,sandwichingadielectricthinfilm;thisstructurestrongly localizestheelectricfieldinthisfilmandhasahighlycapacitivemetaloverlaythatallowsforawiderange offrequencyadjustment.Althoughtheachievedresonancefrequenciesenablealargenumberof appli-cations,asaproof-of-conceptdemonstration,weexperimentallyshowedtheoperationofthiswireless metastructureinHR-MRItohighlightitsprecisefrequencyadjustmentandsignal-to-noise-ratio(SNR) improvementcapabilities.TheproposedmetamaterialwasfoundtomaintainshighQ-factorsdespite loadingwithabody-mimickinglossyphantom.Theexperimentalresultsindicatedthattheproposed metastructurecanbeusedasanSNR-enhancingdeviceoffering15-foldSNRenhancementsthatallows forimagingofobjectsassmallas200␮mindiameterinitsvicinity,atanunprecedentedlevelof resolu-tionatthegivenDCfieldusingstandardheadcoils.Asaresultofitsdeep-subwavelengthminiaturization accompaniedbyreasonableQ-factorwithoutstandingresonancefrequencyadjustmentcapability,this classofmetastructureisprovedtobeanexcellentcandidateforinvivomedicalapplications.

1. Introduction

FollowingtheseminalworkofVeselago[1],metamaterialshave beenintroducedindifferentapplicationsincludingmaterial char-acterization[2],sensing[3–8],compactingdevices[9]andimaging ofsubwavelengthfeatures[10],spanningfromopticalfrequencies [11]totheradiofrequency(RF)region[12].Theoperating band-widthof thosemetamaterial devices hasbeentypicallynarrow becauseofthehighqualityfactor(Q-factor)elementsusedinthe unitcelloftheirstructures.Becausemagneticresonanceimaging (MRI)isbasicallyanarrowbandwidthimagingtechnique, meta-materialscouldbequiteattractiveforuseinMRIapplications.It

∗ Correspondingauthorat:DepartmentofElectricalandElectronicsEngineering, DepartmentofPhysics,NationalMagneticResonanceResearchCenter(UMRAM), BilkentUniversity,Ankara,TR-06800,Turkey.

E-mailaddress:sayim@ee.bilkent.edu.tr(S.Gokyar).

waspreviouslyshownthatmetamaterialstructurescanbeusedfor RFﬂuxguiding[13]andsignal-to-noise-ratio(SNR)improvement purposes[14].Thesemetamaterials,inadditiontoconventional imaging hardwareofthescanner,properlymanipulatestheEM ﬁeldsintheirvicinitytoincreaseimagingsignalemittedfromthe imagedobjects(e.g.,tissues).However,thesewirelessdesignsare largerinsizetobeusedformedicalapplications;hence,thedesign ofwirelesssub-cmmetamaterialstoaddressinvivoMRIofsub-mm featureshasnotbeendemonstratedtodate.

High-resolutionMRI(HR-MRI) suffersthefundamental prob-lemofreducedSNRbecauseofthedecreasedvolumeoftheimaged voxels.ToincreasetheSNRofanMRimage,severalmethodscan beapplied.TheseincludeusingahigherDCmagneticﬁeld[15], using highdensitycoil arrays withparallel imaging techniques [16,17],increasingthenumberofimageacquisitionandusing high-sensitivitywiredcoils[18–27].Practically,theDCﬁeldstrengthis predeterminedandassumedtobeconstantaftertheinstallmentof themainmagnet.However,usinghighdensitycoilarrayswith par-https://doi.org/10.1016/j.sna.2018.03.024

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allelimagingtechniquesisoneofthemajorbreakthroughs;their performancescanbeincreasedbyusingwirelesscoilsforinvivo applications.Increasingthenumberofacquiredimagesincreases theimaging duration and total RF powerexposure of patients, whichisnotsuitablefor clinicalimaging practices.Hence,for a predeterminedDCfieldandareceivercoilconfiguration,increasing SNRwithoutincreasingthetotalRFpowerexposureandimaging durationbecomespossiblewithlocalizedcoilsolutions. Unfortu-nately,thesecoils[18–28]requirecomplicated electronics(e.g., matchingcapacitors,solder,diodesand/orcryo-coolingetc.)and theyareconnectedtothebodyofthescannerviaRFcables.Hence, theirapplication toinvivo operationsis inherentlychallenging becauseof RF heating risks [29]. Using wireless resonators for invivoMRIapplicationswouldincreasethedetectionperformance ofanMRIsystem[13,14,30–32].Therehasbeensignificanteffortin theliteraturetodecreasetheresonancefrequency(f0)of metama-terials[33]suchas,increasingthesizeoftheelementsgiveninthe slab[34]and/orusinglumpedcapacitors[12]tocapacitivelyload theunitcells.Althoughmostofthesemethodsareacceptablefor certainapplications,suchasstrainsensing[35],theyarenot suit-ableforinvivoapplicationsbecauseoftheirsize[34]andlumped capacitorsusedtotunetheirresonancefrequencies[12].However, noneofthepreviouswirelessdesigns,ormetamaterials,achieved theelectricalsizeofsmallerthan␭/300andaQ-factorofmorethan 50simultaneouslywithoutusingcryo-coolingoralumpedelement thusfar.

In this work, to address the aforementioned problems of HR-MRI,wedemonstrateawirelessdeep-subwavelength metas-tructureenablingaQ-factorofapproximately80infreespace,in ahighlycompactfootprintarea.Heretheproposedwireless meta-materialstructure,whilebeingelectricallyverysmall,isalsoshown tobeanexcellentcandidateforinvivoMRIapplicationsincluding HR-MRIatsub-mmresolution.

2. Methods

Theproposedstructureisacross-viametallizeddouble-layer metamaterial,inwhichtheconsecutivemetallayersarestrongly coupled (i.e. both inductively and capacitively) to each other throughanoverlayregiontodecreasetheresonancefrequencytoa pre-deﬁnedfrequency.Fig.1.ashowsaschematicoftheproposed structure. Conductive cross-via metallization results in a thin-ﬁlm loaded semi-turn over-laid double-layer resonator. Unlike theclassicalsplitringresonators(SRR)andmulti-layerSRRs,this metamaterialstructureexhibitshigherinductivecouplingviathis cross-viametallizationbetweenconsecutivelayers.

2.1. Equivalentcircuitmodelingandfull-wavenumericalanalysis EquivalentcircuitmodelsofSRRs[36]andspirals[37]havebeen previouslyreportedintheliterature,wherethesinglelayer res-onatorsaremodeledasa seriesRLCcircuitwithpropermutual couplingterms.ResonancefrequencyofaresonatorisgivenbyEq. (1)

f0= 1 2

LeffCeff

(1) whereL_effistheeffectiveinductanceandC_effistheeffective capac-itanceoftheoverallstructure.Q-factorofaseriesresonatorisgiven byEq.(2) Q=2f0Leff Reff = 1 Reff

Leff Ceff = f0 f3dB (2) whereR_effistheeffectiveresistanceandf3dBisthe full-width-half-maximum(FWHM)bandwidthoftheresonator.Unlikepreviously

Fig.1.Schematicrepresentationoftheproposedwirelessmetamaterialstructure (notdrawntoscale).(a)Ametal-insulator-metal(MIM)devicewithcross-via met-allizationtoincreaseLeffinagivenfootprintarea(withsemi-turnoverlay).(b)The operationofthestructurecanbemodeledbyusingacascadedequivalentcircuit approach.Eachunitcelliscomposedofdifferentialinductance(dL),capacitance (dC)andresistance(dR)withamutualcouplingofdMforpartialoverlayregions.

studied structures, this metamaterial architecture is composed oftwoinductivelayersconnectedinseries(viacross-via metal-lization)withstrongcapacitivecoupling,resultingindistributed thin-ﬁlmcapacitancebehaviorthatcannotbeanalyzedusing con-ventionalmethods[40,41].

Beforewemodeltheproposedarchitecture,wecalculatedthe inductanceofasingleturnrectangularresonator,L0,byusingEq. (3) L0=0.6350rn2Dav

ln

_2.07

+0.18+0.132

₍₃₎ andtheparallelplatecapacitance,C0,byusingEq.(4)

C0=ε0εrA

d (4)

where␮0isthepermeabilityofthefreespace,␮ristherelative permeabilityofthematerialusedforresonatorfabrication(which hastobeunityforMRIoperation),nisthenumberofturn(unityfor asinglelayerstructure),Davistheaveragediameter(Dav=Do+D₂ i), istheﬁllratio(= Do−Di

Do+Di),Doistheouterdiameter(sidelength

forrectangularresonators),D_iistheinnerdiameter(side length-2×w)fortherectangularresonators),wisthemetallizationwidth, ␧0isthepermittivityofthefreespace,␧ristherelativepermittivity ofthedielectricusedforelectricﬁeldlocalization,Aistheparallel platesurfaceareaanddisthedistancebetweentheconsecutive layers(e.g.,dielectricthicknessfortheproposedstructure).

Finally,theACresistanceofthesingleturnstructureis calcu-latedbyusingEq.(5)

R0= l

wı(1−e−tmetal/ı) (5)

wherelisthemeantpathlengthofthemetaltrace(proportionalto thenumberofturns,n),t_metalisthethicknessofthemetallization, ␴istheconductivityofthemetalusedforfabricationand␦isthe

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skin-depthofthemetalforthegivenfrequencythatisformulated asgiveninEq.(6). ı=

2 2f (6)

Stackingadditionalturnsdoesnotchangetheﬁllratio,␳.Thus, WhenwesubstituteEqs.(3)and(5)intoEq.(2),weobservethat theQ-factorislinearlyproportionaltothenumberofturns,n,fora pre-determinedresonancefrequency,f0.Thisisnotthecasefor spiralresonatorsbecauseofdecreasingmutualcouplingamong consecutiveturns[33].

To model its behavior, we discretized the proposed struc-tureton0 unit cells,as depictedin Fig.1b;theseunitcells are cascadedtoconstructtheoverallstructure.Eachunitcellis com-posedofdifferentialinductance(dL=L0/2n0),differentialresistance (dR=R0/2n0),differentialthin-filmcapacitance(dC=C0/n0)and dif-ferentialmutualcoupling(dM,dM=kdL),wherekisthecoupling coefficientandhasavalueofapproximately1forstrongpositive couplingviacross-viaconnection[38].Forelectricallysmall struc-tures(e.g.,electricalsize<␭0/300forthiscase),thecornersofthe proposedstructurecanalsobemodeledbyusingtheaboveunitcell configuration.Similarly,theviametallizationisalsomodeledasa seriesRLcircuit(withoutdCelement)betweenconsecutivelayers. ByusingKirchhoff’scurrentlaw,weconstructedtheadmittance matrixasV[Y]=I,whereVandIarethevoltageandcurrentvectorsof thenodesrespectivelyandYistheadmittancematrixoftheoverall structure(detailsarereportedinthesupplementaryfile,sectionS1). TheresultingimpedancegraphsarecalculatedbyusingaMATLAB® (TheMathWorks,Inc.01760USA)todeterminetheresonance fre-quency(i.e.,calculatedfromthepeaksoftheimpedancegraphs) andtheQ-factor(calculatedusingthe,full-width-half-maximum, FWHM,ofthegraphs)ofthemetamaterialforvariousn0.

Theeffectsofvariousgeometricparameters,includingt_dieland overlayarea,wereanalyzedbyusingafull-wavenumericalsolver, CST-MicrowaveStudioTM_(CST,₆₄₂₈₉_Darmstadt,_Germany)._The simulationdomainwascomposedofacubicvacuumenvironment withasidelengthof16mmandtheboundaryconditionsareset asperfectlymatchedlayers(PMLs)inalldirections.Asquarecoil havingasidelengthof8mm,atracewidthof1mm,anda met-allizationthicknessof35␮mispositioned0.2mmawayfromthe proposedstructuretobeusedasthepick-upcoiltomeasureits inputimpedance.Themetallizationmaterialusedwasgoldforboth theantennaandtheresonator.Thedielectricmaterialofthe pro-posedstructurewaschosenaslossypolyimidefromthelibrary ofCSTMicrowaveStudio,forfull-wavesolutions.Thefrequency domainsolverwasusedtoacquirethescatteringparametersof thewirelessstructure.Thissimulationenvironmentisdepictedin Fig.2.Here,wefollowedthemethodsdescribedbyGinefrietal. [39]andmeasuredtheinputimpedanceusinganetworkanalyzer (AgilentE5061B)andapick-upcoilantenna(detailsarereportedin thesupplementaryﬁle,sectionS2).

2.2. Microfabricationofmetastructures

Wefabricatedtwo differentdevices(rigid andflexible ones) withdifferentmicrofabricationmethods.Therigiddevicesaimto achieve thesmallestelectricalfootprint area(without targeting apredefinedoperationalfrequency)fora wirelessmetamaterial structure,where andtheflexibledeviceismicrofabricatedonto apolyimidesubstrateandtunedtoapredefinedMRIfrequency. Therigidsamples,presentedinFig.3(a),aremicrofabricatedonto a<111>siliconsubstrate.Byusingahard-maskwith complemen-tarySRRpatterns,wethermallyevaporatedtwo10␮mthickAu SRRlayers(heregoldischosenbecauseitisbiocompatible)witha

Fig.2. Schematicrepresentationofthemeasurementsetup(notdrawntoscale). Theresonatorisstronglycoupledtothepick-upcoilantennatomeasureits char-acteristicproperties.

Fig.3.Opticalphotographsofthemicrofabricateddevices.(a)Rigidsampleshave thefootprintof6mm×6mm(foreachfeature).Thesesamplesaremanufactured inarrayformontoasiliconwaferwitha1-␮mthicksiliconnitridedielectric sandwichedbetweentwo10-␮mthickgoldlayers.(b)Theflexiblestructureis microfabricatedontoapolyimidethinfilmwithsub-cmdimensions(8mm×8mm). 1_␮mthickplasma-enhanced-chemical-vapor-deposited(PECVD) siliconnitride(Si3N4)sandwichedbetweeneachofthegoldlayers. Thesecondsample,presentedinFig.3(b),ismicrofabricated ontoan8mm×8mmfootprintareabyusingaflexiblepolyimide film(Kapton®)withaninitialthicknessof7.5␮m.Theproposed thinfilmisthinnedto2.7␮mbyusingreactiveionetching(RIE), with the following recipe: SF6:O2 of 45:15 sccm at 150W RF power,with25mTorrpressuretoincreasetheeffectivecapacitance betweenconsecutivelayers.Byusingahard-maskwith comple-mentarySRRpatterns,wethermallyevaporatedtwo10-␮mthick AuSRRlayerswithasymmetriccombsizes,withonelayeroneach sideofthepolyimidefilm,andintroducedviametallizationthrough thesubstratecross-connectingapairoftheoppositeedgesofeach SRRontheotherside.Subsequently,thesampleswereannealed at 250◦C for 5min for increased electrical conductivity.Unlike conventionalopticallithographytechniquesusedinrigidsample fabrication[40],thismethodpreventspotentialchemicalhazards forbiocompatibilityanddrawsthesimplestmethodologyforhigh yieldfabrications.

2.3. MRIsetup

To demonstrate the MRI operation of the proposed ﬂexible metamaterialstructure,wepreparedagel-phantomwith dimen-sions80×80×40mm3_by_using₁_g/L_NaCl,_2.5_g/L_CuSO

4and14g/L agarose-geltomimicthetissueproperties[41]witha correspond-ingrelativepermittivityofapproximately60andaconductivityof 0.5S/m.Twosetsofevenlydistributed13ﬁberpillars,eachpillar withadiameterof200␮m,wereimmersedintothepre-mentioned gelphantomandpositionedalong ˆz-directionwithdepthsof0.1 and5.0mmfromthephantomsurface(Fig.4).Hereweacquired the2-DMRimagesperpendiculartotheorientationofthepillar

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Fig.4. SchematicrepresentationoftheMRIimagingsetup(notdrawntoscale).A phantomwithtwosetsofpillars,whereeachsethas13evenlydistributedpillars with200-␮mdiameterandsetsareseparatedby5mmapartfromeachother,is locatedinsidea12-channelheadcoil.Theproposedmetamaterialispositionedon topofthephantomtoimagethepillarsinitsvicinity.

array(i.e.,transverseplaneistheXYplanefor ˆz-directedpillars)by usingspoiledgradientecho(GRE)imagingsequencewithanEcho Time(TE)/RepetitionTime(TR)of9.25ms/100ms,afieldofview (FOV)of34_×34mm,animagingmatrixof512_×512,animaging durationof4min19s,apixelbandwidthof180Hz,aflipangleof 3◦andaslicethicknessof2mm.Thisimagingconfiguration cor-respondstoabout66␮mspatialresolutionattheimagingplane. Alloftheexperimentswereconductedbyusingstandardtwelve channelheadcoilsofa3TSiemensMagnetomTim-Trioscanner.

Theworkingprincipleoftheproposedmetamaterialstructure canbeexplainedintwo parts:1)theinductivecouplingofthe transmit-field(bodycoilsforthis imagingconfiguration)and2) thereceive-fieldinductivecoupling.Thisstructureconcentrates thefluxinitsvicinitythatistransmittedduringtheexcitationstage, whichiscalledtransmit-fieldcoupling.Inresponsetothis over excitation,excitedspinsinducessurfacecurrentsonthis metama-terialandthemetamaterialinductivelytransmitsthesesignalsto thereceivercoils(headcoilsforthisimagingconfiguration),which iscalledthereceive-fieldcoupling.

3. Resultsanddiscussions

3.1. ResonancefrequencyandQ-factorcalculations

TheEffective capacitanceof thestructureis strongly depen-dentonthedielectricthickness,t_diel,andthesurfaceareaofthe thin-ﬁlmloadedhelicaltraces.Thissurfacearea, alsocalledthe overlayregion,alsoaffectstheeffectiveinductance,L_eff,because ofincreased ordecreased thenumber of turns.Partial removal of oneof the layers (e.g.,thetop layeris partially removed in Fig.1)resultsin decreased L_eff and C_eff,thereby increasingthe increasedresonancefrequency.Theeffectofpartialthin-ﬁlm load-ingisnumericallyanalyzedfordifferentdielectricthicknessesby usingCSTMicrowaveStudio.TheseresultsaredepictedinFig.5. Theresonancefrequencyrangeof65MHzto5.5GHzisfoundto beachievableforthesamefootprintareawiththegivendielectric thicknesses(i.e.,8mm×8mmwith2.5-␮mthickpolyimide).

Resonancefrequencyadjustmentofself-resonantdesigns(i.e, designsthatdonotincludelumpedelements)toapredeﬁnedMRI frequencyisnotpracticalformostofthecases.Unlikethe previ-ouslystudiedchiralmetamaterialstructures[42]orstacked-SRR typedesigns[43],heretheproposedgeometryallowsusto

eas-Fig. 5.Resonance frequency adjustment capability of the ﬂexible design for 8mm×8mmfootprintarea(notdrawntoscale).Forfullyloaded(doubleturn) helicalringgeometry,itispossibletoreachlowerresonancefrequencies.Partial removalofthemetallizationlayer(upperlayerforthisconﬁguration)resultsin increasedresonancefrequencyviadecreasedeffectiveinductanceandcapacitance. 100%percentetchedareacorrespondstoasinglelayerSRR,wheretheresonance frequencyincreasedto5.5GHz.

Fig.6.Inputimpedanceoftheproposedmetamaterial,withafootprintareaof 8mm×8mmanddielectricthicknessof2.7␮m,forthegivenequivalentcircuit modelforvariousdiscretizationnumbern0.Theresultsareconvergent,andeven usingn0=10providessigniﬁcantlyaccurateresults.

ilyincreasetheresonancefrequencyafteritsmanufacturing,by usingthemetallizationremovalmethodforparallelplatecoils[18]. AsdepictedinFig.5,removalofthemetaloverlayresultsinboth decreasedthin-ﬁlmcapacitancebetweenconsecutivemetal lay-ersanddecreasedeffective-inductanceduetoloweredthenumber ofturns.Hence,theresonancefrequencyoftheproposed meta-materialstructurecanbeconvenientlyincreasedtoapredeﬁned resonancefrequency.

AsproposedinSection2.1,theequivalentcircuitmodelforthe givenﬂexiblemetastructurewithafootprintareaof8mm×8mm isanalyzedtodeterminetheresonancefrequencyandtheQ-factor forvariousnumberofdiscretization.Fig.6depictstheimpedance graphsforvariousdiscretizationnumbers,n0.Theacquired reso-nancefrequenciesandQ-factorscalculatedbyusingtheFWHMof thesegraphsarealsoreportedonTable1.

Here,weobservedthattheincreasingthediscretization num-beroftheproposedarchitectureconvergestothef0of64MHzand Q-factorofapproximately46,inreasonableagreementwiththe experimentalresultsfoundas65MHzand42fortheresonance frequencyandtheQ-factorrespectively.Byusingconventional for-mulae(i.e. f0=1/(2

Lef fCef f, withL0=15.1nH, C0=303pF, andR0=0.16),wecalculatedthef0of74.4MHzandaQ-factor

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Table1

Performance metricsof theproposedmetastructure,with a footprintareaof 8mm×8mmanddielectricthicknessof2.7-␮m,duetodifferentdiscretization number(n0). n0 f0(MHz) Q-factor Time(s) 1 45 36 0,1 2 60 44 0,1 10 64 46 0,1 100 64 46 3,1

Fig.7. Impedancegraphsforthe8mm×8mmsample.Real(top)andimaginary (bottom)partsofthecompleximpedancesshowthattheproposedequivalentcircuit modelestimatestheresonancefrequencyandtheQ-factorofthegivenstructure betterthantheconventionallumpedRLCmodelandhasaperformancesimilarto thatofthefull-wavenumericalsolutions.

of36fortheproposedmetastructure.Finally,f0of71MHzand Q-factorof44isobtainedbyusinganumericalfullwavesolver.The impedancegraphsoftheseresultsareshowninFig.7.

Similarly,forthestructurewithafootprintareaof6mm×6mm, aninductanceof9.5nHandacapacitanceof1.6nF(forthegiven silicon-nitridedielectricofrelativepermittivityof8.9andloss tan-gentof0.0006),andaresistanceof0.08isusedtocalculateits operatingfrequency.ThelumpedRLCformulationresultedinf0 of41.2MHzandQ-factorof20,whereproposedequivalentcircuit modelresultedinf0of35.4MHzandQ-factorof26,whicharein reasonableagreementwiththeexperimentalresultsof33.4MHz and13fortheresonancefrequencyandtheQ-factor,respectively. Finally,f0 of35.6MHzandQ-factorof11isobtainedbyusinga numericalfullwavesolver.Theimpedancegraphsoftheseresults arevisualizedinFig.8.

Weobservedthattheproposedequivalentcircuitmodel esti-matestheresonancefrequencyofthemetastructure,betterthan conventionalcalculationmethods. Additionally,weseethatthe proposedthin-ﬁlm loadedgeometry neitherbehavesas a sim-ple series resonator, nor like a parallel resonator: rather, it is a cascaded RLC circuit with proper feedback (i.e., feedback in electricalmodelcorrespondstoaphysicalconnectioncalled cross-via-metallization)toprovide better resonancebehavior. Hence, theproposedcascadedequivalentcircuitmodelcharacterizesthe

Fig.8. Impedancegraphsforthe6mm×6mmsample.Real(top)andimaginary (bottom)partsofthecompleximpedancesshowthattheproposedequivalentcircuit modelestimatestheresonancefrequencyandtheQ-factoroftheproposedstructure betterthanconventionallumpedRLCmodelandhasaperformancesimilartothat ofthenumericalfull-wavesolver.

behaviorof thestructure moreaccuratelycomparedto conven-tional lumped-element based methods. Because the proposed circuitmodelcannotincludetheeffectofsurroundingmedium, which requiresfull-wavesimulations,it cannotestimatethe Q-factorcorrectly.Hence,calculationofQ-factorunderlossymedium, suchasloading,mightnotbereliableforthegivencircuitmodel, asisalsothecasefortheconventionallumpedRLCmodels.

In the impedance graphs presented in Fig. 8, we found the resonancefrequencyoftherigidmetamaterial(6mm×6mm res-onatorsandwichinga1-␮mthicksilicon-nitride)tobe33.4MHz withacorrespondingfree-spacewavelength(␭0)of8.98m. We calculated that thesidelength ofthe rigidresonator(6mm)is shorterthan␭0/1500,whichisoneofthesmallestsingle-chip deep-subwavelengthresonatorsreportedthusfarintheliterature[44]. Althoughatheoreticalworkwithasidelengthof␭0/1733[45]and anexperimentalworkwithlumpedcapacitorshavingasidelength of␭0/2000[46]werereported,thereis noexperimental demon-strationforawirelessself-resonantstructure(i.e.,withoutlumped element)electricallysmallerthanthestructurepresentedhere. 3.2. Resonancefrequencyadjustmentoftheﬂexiblesampletoa pre-deﬁnedmrifrequency

To achieve the resonance frequency near a predeﬁned MRI frequency(123MHzforour3TMRIscanner)weusedoptical lithog-raphy to precisely etch the necessary amountof metal on the overlay.Weobservedthatetching17.5mm2_on_the_overlay (cor-respondstoapproximately63%etchedareaofconsecutivelayers) resultedinaresonancefrequencyof126MHz,whichwasin agree-mentwiththenumericalresultsprovidedinFig.5.Themeasured Q-factoroftheﬂexiblemetamaterialwasalsoincreasedfrom42 toapproximately82,whichwasinagreementwithQ=2f0Leff/R viatheincreasedresonancefrequency.Itwaspreviouslyreported thattheQ-factorofconventionalstructures,(e.g.,spirals,solenoids

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Table2

Experimentalcharacterizationresultsfordifferentsamples.

Type Dielectric(thickness) EtchRatio(%) f0(MHz) Q-factor

Rigid(6×6mm2₎ _Si

3N4(1␮m) 0 33.4 13

Flexible(8×8mm2₎ _Polyimide_(2.7_␮m) ₀ _65.0 ₄₂

Flexible(8×8mm2₎ _Polyimide_(2.7_␮m) ₆₀_(tuned) _126.0 ₈₂

Flexible-Loaded(8×8mm2₎ _Polyimide_(2.7_␮m) ₆₀_(tuned) _123.5 ₆₄

Fig.9. Numericalresultsshowtheelectricfieldconfinementpropertyoftheproposedmetamaterialstructurewithafootprintareaof8mm×8mm.Theelectricfield distributionclearlyindicatesthattheE-fieldisstronglyconfinedbetweenthetopandbottomlayers,leadingtohigherQ-factorevenwhenloadedinalossymedium.(a) Amplitudeoftheelectricfieldnormalizedtotheincidentfieldalongwiththedashedlinemarkedin(b)showingthattheelectricfieldis6ordersofmagnitudehigherinthe localizedregiononresonancewithrespecttotheincidentfield.

andSRRs)donotincreaselinearlybecauseofreducedinductance (andthereducedmutualinductance)fortheconsecutiveturns[33]. However,theproposedgeometryprovidesalmostalinearQ-factor improvement,viathestrongmutualcouplingamongconsecutive layers.Thus,thisstructureisveryspecialintermsofhigherQ-factor andloweredresonancefrequencyforasmallerfootprintarea.

Thetunedresonatorwasimmersedintotheabovementioned phantom,asdescribedinSection2.3,anditswirelessimpedance wasmeasuredbyusingthesamepick-upcoilandmethod[30]. TheloadedQ-factor for this conﬁguration wasmeasuredas 64 accordingtotheFWHMofthecompleximpedance.Theresultsare summarizedinTable2forcomparison.

3.3. Electricfieldconfinementforimprovedloadingperformance Topermituseatextremely subwavelengthfrequencies, con-ventionalresonators(such asSRRs,spiralsetc.)requirelumped capacitorstotunetheirresonancefrequencies.Theelectricfield distributionofthesestructurespillsoverfromtheirplanebecause oftheselumpedcapacitors,resultinginvulnerabilitytoexternal effectssuchasloadingwithalossytissue(seedetailsarereportedin thesupplementaryfile,SectionS3).Theuseofthedouble-layer heli-calgeometryprovidesanadvantageofelectricfieldlocalizationin thelower-lossdielectricregion(comparedtolivingtissues)that allowsforhigherQ-factor.Fig.9(a)presentsthe|E|-fieldprofile ofthemapnormalizedtoincidentfield( E_˙I)alongwiththedashed linemarkedinFig.9(b),whereincidentfieldistheelectricfield intensityrecordedattheexcitationportofthesimulationdomain. Weobservedthattheelectricfieldis6ordersofmagnitudehigher inthelocalizedregionunderresonanceconditionmatchedtothe MRIfrequencycomparedtotheincidentfieldandalmost3orders ofmagnitudehighercomparedtotheoff-resonancecase.Fig.9(b) indicatestheabsolutevalueoftheelectricfield distribution(|E| map)localizedinthedielectricregionbetweenthetopand bot-tommetalliclayers.Clearlytheelectricfieldisstronglyconfined betweenthemetallizationlines;thisstrongconfinementis essen-tialtoachievinghighQ-factorevenwhenloadedinalossymedium includingbiologicaltissues.

Livingtissuesexhibithigherconductivelosses,e.g.,conductivity of1S/m,whereasthedielectricshaveradicallylower conductivi-ties,e.g.,conductivityof10−16S/mforaKapton®.Theproposed metamaterialdeviceconﬁnestheelectricﬁeldinsidethedielectric material,insteadoflivingtissues,therebydrasticallydecreasingthe dissipatedresistivepoweratthegivenfrequencywhenthe metas-tructureisplacedinalossymedia.Thispropertyhelpstomaintain theQ-factorofthemetamaterialdevice,evenwhenthe metastruc-tureisloadedinvivo.Hence,theproposeddeep-subwavelength metamaterialexhibitsthesepropertiesforwirelessoperationthat arecriticaltoinvivostudies.

3.4. MRIcharacterization

The proposedstructure was locatedon a coronal plane(XZ plane),whereimmersedpillarswerealignedinthe ˆz -direction, andthesamplewaslocatedinsideastandardheadcoilofthe scan-ner,asshowninFig.10(a).Transverseimages,withtheimaging parametersgiveninSection2.3,wereacquiredtocounteachand everypillarasshowninFig.10(b).Here,weobservedthatthepillar arraycanbevisibleonlyinthevicinityoftheresonator,in agree-mentwiththeB1+ mapofthewirelessmetastructureasshown inFig.10(c).TheB1+resultsshowedthattheamplitudeoftheRF magneticfieldcanbeamplifiedsignificantlyinthevicinityofthe resonator.FromtheMR imagegiven inFig.10(b),we obtained theintensityplots alongblueand redlinesmarkedonit.From Fig.10(b),weselectedaregionwithasizeof100×100pixelsthat doesnotcontainanyMRIsource(i.e.noiseregion),andcalculated theaveragenoiseleveltobeapproximately50arbitraryunits(a.u.), wherethesignalintensityintheneighboringregionofthe res-onatorappearstobeapproximately1000a.u.Theintensitycurve inblue,dropstoapproximatelynoiselevelforthecorresponding pillarsinthevicinityofthemetamaterialresonator.Wecanclearly countthenumberofdipsas13,whichisthenumberofpillarsin thearray.Theredcurve(at5mmaway)showstheintensityprofile farawayfromtheresonator(Fig.10-d).Clearly,thepillars5mm awayfromthemetamaterialarenotvisuallyseparablefromeach other.

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Fig.10.MRIcharacterizationofthetunedmetamaterial,withthefootprintareaof8mm×8mmusedtoresolvetheevenlydistributedpillarswithadiameterof200␮m.(a) 3TSiemensMagnetomTrioimagingsystemisusedwithaheadcoil;thesystemisloadedwithabodymimickingphantomtoimagefibersimmersedinthephantom.(b)MRI imageshowingthatpillarsareclearlyvisibleandcanbecountedinthevicinityoftheresonatoralongtheblueline(at0.1mmawayfromthemetastructure),whereasthey arenotfullyresolvablealongtheredline(5mmawayfromthemetastructure).(c)B1+mapofthewirelessmetamaterialstructureshowingsignificantB1+amplificationin itsvicinity.(d)Thered(dashed)curveindicatestheimageintensitypatternat5mmawayfromthedeviceandtheblue(solid)curveindicatestheimageintensityat0.1mm awayfromthedevice.Theblue(solid)profileclearlyresolves13ofthepillars(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothe webversionofthisarticle).

Herewealsoseethatthesignalintensityisampliﬁed approx-imatelyoneorderofmagnitude(1000/100)inthevicinityofthe metastructure.Forthepillarsclosetotheresonatormetallization, thecontrast-to-noise-ratio(CNR)reachestoapproximately15.4 (e.g.,CNR=920−150

50 ), whereCNRdropstoapproximately6.9for the6thand7thpillarsbecauseoftheincreasedSNRinthe proxim-ityofthemeta-device,veriﬁedbyitsB1+map.Forthepillarsaway fromtheresonator,theCNRdropstoapproximatelyunity,which ismeaningless.Toimagesmallobjects,e.g.,pillarswith200␮m diameter,theSNRshouldbekepthighenoughtoeliminatenoise effects.TheproposedmetamaterialstructuremanipulatestheEM ﬁeldstronglyinitsvicinitytoincreasetheSNR,allowingforMRIof sub-mmpillarswithanunprecedentedresolutionfor3Theadcoils thatisotherwisenotpossibleusingtheseimagingparameters.

4. Conclusion

Inconclusion,weproposed,modeledanddemonstrateda wire-less compact metamaterial architecture with a side length of approximately␭0/1500andfrequencyadjustmentrangeof65MHz to 5.5GHz. This proposed metastructure possess a Q-factor of approximately80for123MHz.Wedemonstratedthatthis deep-subwavelength metamaterialcan beusedas anSNR-enhancing deviceforMRI.Becauseofitsstrongelectricﬁeldconﬁnement prop-ertyinitsdielectricregion,theproposedstructureexhibitshigher Q-factorseveninalossymedium(i.e.,livingtissues).Therefore, thiswirelessmetastructureisanexcellentcandidateforusein

var-iousapplicationsincludinginvivoMRimagingplatformsandsmart implants.

Acknowledgements

HVD gratefullyacknowledgessupportfromTÜBA. Thiswork ispartiallysupportedbyTurkishNationalScientiﬁcand Techno-logical Research InstituteTÜB˙ITAK-B˙IDEB. Authorsof this work gratefullyacknowledgethesupportofUNAM-National Nanotech-nology Research Center and Instituteof Materials Science and Nanotechnology.

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Biographies

Sayim GokyarcompletedhisPh.D. atBilkent Univer-sity,DepartmentofElectricalandElectronicsEngineering, Ankara.Hisresearchinterestsincludewirelesssensors anddesigningimplantableelectronicdevicesforwireless imagingapplicationsaswellasforsensing.

AkbarAlipourcompletedhisPh.D.atBilkent Univer-sity,DepartmentofElectricalandElectronicsEngineering, Ankara.Hisresearchinterestslieintheareaofthin-ﬁlm microwavestructureswhichareusedformagnetic res-onanceimaging(MRI)markingandwirelesssensing.He hasbeeninvolvedinthedevelopmentofdeviceswhichare mainlyusedininterventionalMRIandmedicalimplants.

EmreUnalreceivedhisB.S.degreeinelectricaland elec-tronicsengineeringfromHacettepeUniversity,Ankara, Turkey,in2005.Heisafull-timeResearchEngineerunder thesupervisionofProf.H.V.DemirwiththeInstituteof MaterialsScienceandNanotechnology,Bilkent Univer-sity,Ankara,whereheisworkingonthedevelopmentof microwaveandoptoelectronicdevices.

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ErginAtalarreceivedhisB.S.degreefromBogazici Uni-versityin1985,M.S.degreefromMiddleEastTechnical Universityin1987,andPh.D.degreefromBilkent Univer-sityin1991,allinElectricalEngineering.Hejoinedthe JohnsHopkinsUniversity,wherehebecameaProfessor ofRadiology,BiomedicalEngineeringandElectricaland ComputerEngineeringandDirectorofCenterforImage GuidedInterventions.Currently,Dr.AtalarisaProfessorof theDepartmentofElectricalandElectronicsEngineering andtheDirectorofNationalMagneticResonanceResearch Center atBilkent University.Themainresearch inter-estsofDr.AtalarareMagneticResonanceImagingand Imageguidedinterventions.In2006,ErginAtalarwonthe TUBITAKscienceaward.

Hilmi Volkan Demir (M’04-SM’11) received the B.S. degree inelectrical and electronics engineeringfrom BilkentUniversity,Ankara,Turkey,in1998andtheM.Sc. andPh.D.degreesinelectricalengineeringfromStanford University,Stanford,CA,in2000and2004,respectively. InSeptember2004,hejoinedBilkentUniversity,where heiscurrentlyaprofessorwithjointappointmentsatthe DepartmentofElectricalandElectronicsEngineeringand theDepartmentofPhysicsandisalsowithUNAM-the InstituteofMaterialsScienceandNanotechnology. Con-currently,heisafellowofNationalResearchFoundation inSingaporeandaprofessorofNanyangTechnological University.Hisresearchinterestsincludethe develop-mentofinnovativeoptoelectronicandRFdevices.Prof.Demiristherecipientof theEuropeanUnionMarieCurieFellowship,theTurkishNationalAcademyof Sci-encesDistinguishedYoungScientistAward(TUBA-GEBIP),theEuropeanScience Foundation-EuropeanYoungInvestigatorAward(ESF-EURYI),andNanyangAward forResearchExcellence.